When I was in graduate school, stat professors would say “ANOVA is just a special case of linear regression.” But they never explained why.
And I couldn’t figure it out.
The model notation is different.
The output looks different.
The vocabulary is different.
The focus of what we’re testing is completely different. How can they be the same model?
Most of the p-values we calculate are based on an assumption that our test statistic meets some distribution. These distributions are generally a good way to calculate p-values as long as assumptions are met.
But it’s not the only way to calculate a p-value.
Rather than come up with a theoretical probability based on a distribution, exact tests calculate a p-value empirically.
The simplest (and most common) exact test is a Fisher’s exact for a 2×2 table.
Remember calculating empirical probabilities from your intro stats course? All those red and white balls in urns? (more…)
Mixed models can account for different spacing in time and you’re right, it entirely depends on whether you treat Time as categorical or continuous.
First let me mention that not all designs can treat time as either categorical or continuous. The reason it could go either way in your example is because time is measured discretely, yet there are enough numerical values that you could fit a line to it. (more…)
As mixed models are becoming more widespread, there is a lot of confusion about when to use these more flexible but complicated models and when to use the much simpler and easier-to-understand repeated measures ANOVA.
One thing that makes the decision harder is sometimes the results are exactly the same from the two models and sometimes the results are (more…)
Structural Equation Modelling (SEM) increasingly is a ‘must’ for researchers in the social sciences and business analytics. However, the issue of how consistent the theoretical model is with the 
data, known as model fit, is by no means agreed upon: There is an abundance of fit indices available – and wide disparity in agreement on which indices to report and what the cut-offs for various indices actually are. (more…)
In this video I will answer a question from a recent webinar, Random Intercept and Random Slope Models.
We are answering questions here because we had over 500 people live on the webinar so we didn’t have time to get through all the questions.
If you missed the webinar live, this and the other questions in this series may make more sense if you watch that first. It was part of our free webinar series, The Craft of Statistical Analysis, and you can sign up to get the free recording, handout, and data set at this link:
http://TheCraftofStatisticalAnalysis.com/random-intercept-random-slope-models